Chapter 24 - The Wave Nature of Light

Transcription

1 Chapter 24 - The Wave Nature of Light

2 Summary Four Consequences of the Wave nature of Light: Diffraction Dispersion Interference Polarization Huygens principle: every point on a wavefront is a source of spherical wavelets Young s double-slit experiment. Rainbows, Anti-Reflection Coatings

3 Light as a Wave If Light is an electromagnetic wave, lets start by looking at how waves behave. Ocean Waves entering a Cove Where the long ocean waves enter the opening of the cove, they spread out in rings, as if from a point. This phenomenon is Diffraction Exactly the same thing happens to sound, and EM waves (light, radio, X-rays etc)

4 24.1 Waves: Huygens Principle and Diffraction Huygens principle: Every point on a wave front acts as a point source; the wavefront as it develops is tangent to their envelope

5 24.1 Waves Versus Particles; Huygens Principle and Diffraction Huygens principle is consistent with diffraction: Large aperture Small aperture

6 24.2 Huygens Principle and the Law of Refraction

7 Huygens Principle and the Law of Refraction Highway mirages are due to a gradually changing index of refraction in heated air.

8 The most bizzare thing you have likely encountered in Physics so far! Young s Double-Slit Experiment

9 24.3 Interference Young s Double-Slit Experiment If light is a wave, there should be an interference pattern.

10 ConcepTest 24.2a Phase Difference I The two waves shown are 1) out of phase by 180 o 2) out of phase by 90 o 3) out of phase by 45 o 4) out of phase by 360 o 5) in phase

11 ConcepTest 24.2a Phase Difference I 1/4λ The two waves shown are 1) out of phase by 180 o 2) out of phase by 90 o 3) out of phase by 45 o 4) out of phase by 360 o 5) in phase The two waves are out of phase by 1/4 wavelength (as seen in the figure), which corresponds to a phase difference of 90 o. Follow-up: What would the waves look like for no. 4 to be correct?

12 Long straight ocean waves Diffracting and creating Interference Patterns as they divide and recombine around an island-strewn coastline Interference Diffraction Plane waves

13 Diffraction of Light by a Double Slit In this example, a laser shone through a piece of paper with two small holes in it. Instead of 2 spots, you see a central bright spot flanked by many alternating minima and maxima Even more Bizarrely, the effect persists when light is sent through the slit ONE PHOTON AT A TIME Diffraction and Interference have now been demonstrated with beams of electrons, atoms, and even Molecules! Try at Home -its easy! Thomas Young used sunlight and black paper

14 24.3 Constructive & Destructive Interference The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).

15 Condition for Bright and Dark Fringes We can use geometry to find the conditions for constructive and destructive interference: (24-2a) (24-2b)

16 Interference Pattern Between each maxima and the minima, the interference varies smoothly.

17 Diffraction Pattern for White Light The position of the maxima (except the central one) depends on wavelength. The first- and higher-order fringes contain a spectrum of colors. This is the principle used in a Spectrograph

18 24.4 The Visible Spectrum and Dispersion Wavelengths of visible light: 400 nm to 750 nm Shorter wavelengths are ultraviolet; longer are infrared

19 Dispersion by a Prism Wavelength dependence of refractive index is why a prism will split visible light into a rainbow of colors. Light rays bend towards the normal when entering a higher index material. Rays bend away from the normal when exiting Shorter wavelengths (Blue) are bent more than long ones (Red) White light separates into its components The angled faces of a Prism amplify the effect

20 The Visible Spectrum and Dispersion The index of refraction of a material varies with the wavelength of the light. This leads to Dispersion - separation of light by frequency or color Useful for things like prisms, spectrographs or diamond rings Terrible for things like Lenses, telescopes, microscopes, spectacles

21 Dispersion in Nature: Rainbows Actual rainbows are created by dispersion and Internal reflection in tiny drops of water. The Rainbow Angle is ~ 42 degrees

22 24.5 Diffraction by a Single Slit or Disk Light will also diffract around a single slit or obstacle.

23 Diffraction by a Single Slit, Aperture or Disk The resulting pattern of light and dark stripes is called a diffraction pattern. This pattern arises because different points along a slit create wavelets that interfere with each other just as a double slit would. The minima of the single-slit diffraction pattern occur when Airey Pattern

24 24.6 Diffraction Gratings A diffraction grating consists of a large number of equally spaced narrow slits or lines. A transmission grating has slits, while a reflection grating has lines that reflect light. The more lines or slits there are, the narrower the peaks. (greater spectral resolution) A normal CD or DVD is an excellent diffraction grating Gratings are more efficient than prisms and have largely replaced them The Bright Iridescent Colors of Birds Feathers are due to Diffraction-Grating effects

25 Diffraction Grating The maxima of the diffraction pattern are defined by Where d is the line spacing, and m is called the order The higher the order, the greater the dispersion, but the spectra get much fainter at the same time.

26 24.8 Interference by Thin Films: from Soap Bubbles to Anti-Reflection Coatings If there is a very thin film of material a few wavelengths thick light will reflect from both the bottom and the top of the layer, causing interference. This can be seen in soap bubbles and oil slicks, for example. The color seen depends on the thickness of the Film, and its refractive index Thin Coatings on Camera Lenses (etc) are used to prevent reflections But only for limited range of wavelength and incidence angle

27 Anti-Reflective Coatings When a light wave is reflected from a surface (A), it changes in phase by a 1/2 cycle. Usually some of the light is transmitted and some reflected A thin layer (film) of a material with intermediate refractive index is deposited on the surface Some light is reflected at this second boundary B. If the thickness of the film is just right, the reflected wave from B will arrive at the surface 1/2 cycle out of phase with the original reflection. The waves cancel out! A certain AR layer only works for a narrow wavelength range, (because it depends on the index)

28 Summary of Chapter 24 In the double-slit experiment constructive interference when destructive interference when Two sources of light are coherent if they have the same frequency and maintain the same phase relationship

29 Summary of Chapter 24 Visible spectrum of light ranges from 400 nm to 750 nm (approximately) Index of refraction varies with wavelength, leading to dispersion Diffraction grating has many small slits or lines, and the same condition for constructive interference as for a pair of slits. Light bends around obstacles and openings in its path, yielding diffraction patterns Light passing through a narrow slit (Diffraction at a narrow slit) will produce a central bright maximum of width Interference can occur between reflections from the front and back surfaces of a thin film, leading to iridescence and Anti-reflection coatings Light whose electric fields are all in the same plane is called plane polarized

30 24.10 Polarization Light is polarized when its electric fields oscillate in a single plane. Consequence of the direction of oscillation of electrons in atoms Light gets polarized when it reflects off surfaces, or is scattered by gases (e.g. the atmosphere) Any electromagnetic wave can be polarized. Another important example is radio waves.

31 Polarizing Filters (polaroid) Polarized light will not be transmitted through a polarized film whose axis is perpendicular to the polarization direction. Polarizing filters are used in Photography, Sunglasses, Science Labs etc. Usually created by stressing plastics while they are still partially melted, creating a preferred direction of vibration for the molecules. Transmitted Blocked

32 Crossed Polarizers If initially unpolarized light passes through crossed polarizers, no light will get through the second one. This can be very useful, as certain special materials can rotate the plane of polarization.

33 Polarization When light passes through a polarizer, only the component parallel to the polarization axis is transmitted. If the incoming light is planepolarized, the outgoing intensity is:

34 Polarization upon Reflection Light is also partially polarized after reflecting from a nonmetallic surface. At a special angle, called the polarizing angle or Brewster s angle, the polarization is 100%. Reflected Light is Horizontally Polarized (24-6a) For light in air, reflecting off water, Brewster s angle is 53 degrees

35 Use of Polarizer to remove Reflections and Glare in Photography (and Everyday life) Without polarizer: (or adjusted horizontally) Reflections in surface of water With Polarizer: (adjusted vertically) Reflections suppressed. The leaves at the bottom of the pond are now visible

36 Polarization of rainbows Rainbows involve reflection and refraction both inside and at the boundaries of the raindrops. The rainbow is 100% linearly polarized The polarization axis is radial to the bow Just rotate your head while wearing polarized sunglasses

37 Why is the Sky Blue? and is it also Polarized? The clear sky is blue due to Scattering by air molecules. Scattering is a directional process. Examine the sky with polarized sunglasses! At 90 from the Sun, the polarization is upto 80%. -so it will look dark!

38 The blue sky is polarized

39 Polarization of the sky reaches its maximum strength at 90 degrees from the sun Go see if you can observe the overall pattern for yourself Its very hard to photograph!

40